I have made a bunch of sinew bows with hide glue and Titebond 3. I prefer TB3 for its ease of use but I haven't seen a whole lot of difference in the rehydration/dehydration dynamic. My bows still lose and gain weight from season to season. As much as 10 pounds. I keep my bows inside but do not control hmidity intentionally. I should for many reasons but don't yet.
I have used shellac and plastic finishes and haven't really seen much difference between the two.
If it were me, and I lived in a high humidity area most of the year, I'd try my best to avoid sinew. I don't like shooting sinewed bows in the summer here in Indiana becasue of their sluggishness then. I go to Cloverdale in June and my go to bow from the past, a sinew-backed static recurve, was noticeably slower.